Lie bialgebras, fields of cohomological dimension at most 2 and Hilbert's Seventeenth Problem
نویسندگان
چکیده
منابع مشابه
Strongly Homotopy Lie Bialgebras and Lie Quasi-bialgebras
Structures of Lie algebras, Lie coalgebras, Lie bialgebras and Lie quasibialgebras are presented as solutions of Maurer-Cartan equations on corresponding governing differential graded Lie algebras using the big bracket construction of Kosmann-Schwarzbach. This approach provides a definition of an L∞-(quasi)bialgebra (strongly homotopy Lie (quasi)bialgebra). We recover an L∞-algebra structure as...
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A Lie algebra L is said to be of cohomological dimension 1, if H(L, M) = 0 for any L-module M . Due to the standard interpretation of the second cohomology group, this is equivalent to the condition that each exact sequence 0 → M → G → L → 0 splits. Of course, the cohomological dimension may be defined via standard devices of homological algebra – e.g. as the minimal length of the projective re...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2017
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2016.12.018